It hardly needs mentioning that almost everything ever discussed on this site would be included in the example above.

The distinction between this and "almost everything on this site" is relevant. This makes this important to address.

I don't think 'play' is a good term, here. "Play" is something humans do to avoid boredom. It is instrumentally useful, but only because of other flaws in our mind design; specifically, intellectual play is useful to break us out of status quo bias, or something like it. Undirected intellectual exercises get us to explore varying sets of assumptions and habits of thought, which can lead to new conclusions, in a way that we're not good at doing when we sit and think through things as thought experiments.

Or in short, without a proposed mechanism I don't see how you can justify the UFAI's desire to experiment with arbitrary activities rather than simulate them internally.